Method for manufacturing quartz crystal resonator, quartz crystal unit and quartz crystal oscillator

ABSTRACT

A contour mode resonator such as a flexural mode, quartz crystal tuning fork resonator, a width-extensional mode quartz crystal resonator, a length-extensional mode quartz crystal resonator and a Lame mode quartz crystal resonator, a quartz crystal unit and a quartz crystal oscillator, and their manufacturing methods are described. As an example, a plurality of individual quartz crystal tuning fork resonators capable of vibrating in a flexural mode are formed in a quartz crystal wafer, with resonance frequency higher than 32.768 kHz, and are capable of vibrating in a fundamental mode, respectively, and also metal films are formed on said tuning fork tines in the quartz crystal wafer by a spattering method or an evaporation method to get said individual quartz crystal tuning fork resonators whose resonance frequency is lower than 32.768 kHz, and the resonance frequency of said individual quartz crystal tuning fork resonators is adjusted by removing a part or all of the metal films formed on said tuning fork tines in the quartz crystal wafer by laser trimming or a plasma etching method.

FIELD OF THE INVENTION

[0001] The present invention relates to a quartz crystal resonator, aquartz crystal unit and a quartz crystal oscillator, and theirmanufacturing methods.

BACKGROUND OF THE INVENTION

[0002] In general, a quartz crystal resonator is housed in a quartzcrystal unit and a quartz crystal oscillator comprises the quartzcrystal unit. For example, a quartz crystal oscillator with a quartzcrystal unit comprising a contour mode resonator such as a quartzcrystal tuning fork resonator, which is capable of vibrating in aflexural mode, is widely used as a time standard in consumer products,wearable time-keeping equipment and communication equipment (such ascellular phones, wristwatches and pagers). Recently, because of highfrequency stability, miniaturization and the light weight nature ofthese products, the need for a smaller quartz crystal unit and a smallerquartz crystal oscillator with a smaller quartz crystal tuning forkresonator, capable of vibrating in a flexural mode and having a highfrequency stability, a small series resistance and a high quality factorhas arisen.

[0003] Heretofore, however, it has been impossible to obtain a quartzcrystal unit and a quartz crystal oscillator because a conventionalquartz crystal tuning fork resonator, capable of vibrating in a flexuralmode can not be obtained with a high frequency stability, a small seriesresistance and a high quality factor when it is miniaturized.

[0004] Moreover, nothing teaches figure of merit M of the presentinvention which has an influence on a frequency stability for a flexuralmode, quartz crystal tuning fork resonator capable of vibrating in afundamental mode and teaches a relationship of an amplification circuitand a feedback circuit which construct a quartz crystal oscillatingcircuit of the present invention, and also, nothing teaches a method ofmanufacturing a quartz crystal tuning fork resonator capable ofvibrating in a flexural mode, a quartz crystal unit and a quartz crystaloscillator of the present invention.

[0005] Likewise, nothing teaches a method for manufacturing a quartzcrystal unit comprising a contour mode resonator such as awidth-extensional mode quartz crystal resonator, a length-extensionalmode quartz crystal resonator and a Lame mode quartz crystal resonator,and their resonators, according to the present invention.

[0006] In addition, for example, there been has a big problem in theconventional quartz crystal oscillator with the conventional quartzcrystal tuning fork resonator, such that a fundamental mode vibration ofthe resonator jumps to a second overtone mode vibration by shock orvibration.

[0007] It is, therefore, a general object of the present invention toprovide embodiments of a contour mode resonator such as a flexural mode,quartz crystal tuning fork resonator, a width-extensional mode quartzcrystal resonator, a length-extensional mode quartz crystal resonatorand a Lame mode quartz crystal resonator, a quartz crystal unit with thecontour mode resonator and a quartz crystal oscillator comprising aquartz crystal oscillating circuit with a flexural mode, quartz crystaltuning fork resonator, capable of vibrating in a fundamental mode, andhaving a high frequency stability, a small series resistance and a highquality factor, and also to provide embodiments of a method formanufacturing the contour mode resonator, the quartz crystal unit andthe quartz crystal oscillator, which overcome or at least mitigate oneor more of the above problems.

SUMMARY OF THE INVENTION

[0008] The present invention relates to a flexural mode, quartz crystaltuning fork resonator, capable of vibrating in a fundamental mode andhaving a nominal frequency of 32.768 kHz, a quartz crystal unitcomprising a contour mode resonator such as a flexural mode, quartzcrystal tuning fork resonator, a width-extensional mode quartz crystalresonator, a length-extensional mode quartz crystal resonator and a Lamemode quartz crystal resonator, and a quartz crystal oscillatorcomprising a quartz crystal oscillating circuit having an amplificationcircuit and a feedback circuit, and also relates to their manufacturingmethods.

[0009] It is an object of the present invention to provide a flexuralmode, quartz crystal tuning fork resonator capable of vibrating in afundamental mode and having a nominal frequency of 32.768 kHz.

[0010] It is an another object of the present invention to provide aquartz crystal unit comprising a contour mode quartz crystal resonator.

[0011] It is a further object of the present invention to provide aquartz crystal oscillator comprising a quartz crystal oscillatingcircuit with a flexural mode, quartz crystal tuning fork resonator,capable of vibrating in a fundamental mode, and having a nominalfrequency of 32.768 kHz, a high frequency stability, a small seriesresistance R₁ and a high quality factor Q₁.

[0012] It is a still further object of the present invention to providea method for manufacturing a plurality of individual quartz crystaltuning fork resonators capable of vibrating in a flexural mode, a quartzcrystal unit comprising a contour mode quartz crystal resonator, a caseand a lid, and a quartz crystal oscillator comprising: a quartz crystaloscillating circuit comprising; an amplification circuit comprising anamplifier at least and a feedback circuit comprising a flexural mode,quartz crystal tuning fork resonator and capacitors at least.

[0013] According to one aspect of the present invention, there isprovided a method for manufacturing a plurality of individual quartzcrystal tuning fork resonators each of which is capable of vibrating ina flexural mode, and each of the individual quartz crystal tuning forkresonators comprising the steps of: forming integrally tuning fork tineseach of which has a length, a width and a thickness and the lengthgreater than the width and the thickness, and a tuning fork base;providing grooves; and disposing electrodes inside the grooves and onsides of said tuning fork tines, and the grooves being provided at saidtuning fork tines, and the electrodes being disposed opposite each otherinside the grooves and on the sides of said tuning fork tines so thatthe electrodes disposed opposite each other are of opposite electricalpolarity and said tuning fork tines are capable of vibrating in inversephase, wherein the individual quartz crystal tuning fork resonators areprovided in a quartz crystal wafer with resonance frequency higher than32.768 kHz, each of which is capable of vibrating in a fundamental mode,and next, metal films are formed on said tuning fork tines in the quartzcrystal wafer by a spattering method or an evaporation method so as toget the individual quartz crystal tuning fork resonators each of whichhas resonance frequency lower than 32.768 kHz, and wherein comprisingthe further steps of: adjusting the resonance frequency by removing apart or all of the metal films formed on said tuning fork tines in thequartz crystal wafer by laser trimming or a plasma etching method andinspecting the individual quartz crystal tuning fork resonators in thequartz crystal wafer, and when there is a failure resonator therein, itis removed from the quartz crystal wafer or something is marked on it orit is remembered by a computer.

[0014] According to a second aspect of the present invention, there isprovided a method for manufacturing a quartz crystal unit comprising acontour mode quartz crystal resonator which is one of awidth-extensional mode quartz crystal resonator, a length-extensionalmode quartz crystal resonator and a Lame mode quartz crystal resonator,a case and a lid, and said contour mode quartz crystal resonatorcomprising the step of: utilizing a particle method or a chemicaletching method to form a resonator comprising; a vibrational portion;connecting portions located at ends of said vibrational portion;supporting portions connected to said vibrational portion through saidconnecting portions; and electrodes disposed opposite each other onupper and lower faces of said vibrational portion so that the electrodesdisposed opposite each other are of opposite electrical polarity,wherein a plurality of individual contour mode quartz crystal resonatorsare formed in a quartz crystal wafer, each of which is capable ofvibrating in a contour mode and a single mode, and wherein each of saidindividual contour mode quartz crystal resonators is mounted at amounting portion of a case, and the resonance frequency of eachresonator is adjusted by laser trimming or a plasma etching method sothat a frequency deviation is within a range of −100 PPM to +100 PPM toa nominal frequency of less than 135 MHz when the quartz crystal unit isprovided.

[0015] According to a third aspect of the present invention, there isprovided a method for manufacturing a quartz crystal oscillatorcomprising: a quartz crystal oscillating circuit comprising; anamplification circuit comprising an amplifier at least and a feedbackcircuit comprising a quartz crystal tuning fork resonator and capacitorsat least, said quartz crystal tuning fork resonator comprising the stepsof: forming integrally tuning fork tines each of which has a length, awidth and a thickness and the length greater than the width and thethickness, and a tuning fork base; providing grooves; and disposingelectrodes inside the grooves and on sides of said tuning fork tines,and the grooves being provided at said tuning fork tines, and theelectrodes being disposed opposite each other inside the grooves and onthe sides of said tuning fork tines so that the electrodes disposedopposite each other are of opposite electrical polarity and said tuningfork tines are capable of vibrating in inverse phase, and said quartzcrystal oscillating circuit comprising the step of connectingelectrically said quartz crystal tuning fork resonator, the amplifierand the capacitors at least, wherein said quartz crystal tuning forkresonator is capable of vibrating in a flexural mode and said quartzcrystal oscillating circuit comprises said quartz crystal tuning forkresonator whose figure of merit M₁ of a fundamental mode vibration islarger than figure of merit M₂ of a second overtone mode vibration tosuppress the second overtone mode vibration and to get a high frequencystability for the fundamental mode vibration.

[0016] According to a fourth aspect of the present invention, there isprovided a method for manufacturing a quartz crystal oscillatorcomprising: a quartz crystal oscillating circuit comprising; anamplification circuit comprising a CMOS inverter and a feedbackresistor, and a feedback circuit comprising a quartz crystal tuning forkresonator capable of vibrating in a flexural mode, resistors andcapacitors, said quartz crystal tuning fork resonator comprising thestep of: utilizing a chemical etching method to form a resonatorcomprising; tuning fork tines each of which has a length, a width and athickness and the length greater than the width and the thickness, and atuning fork base, and electrodes disposed on obverse and reverse facesand on sides of said tuning fork tines so that said tuning fork tinesare capable of vibrating in inverse phase, said quartz crystal tuningfork resonator being formed in a quartz crystal wafer and a plurality ofindividual quartz crystal tuning fork resonators capable of vibratingeach in a fundamental mode being formed therein, each of whichcomprises: tuning fork tines and a tuning fork base; and electrodesdisposed on obverse and reverse faces and on sides of the tuning forktines, and has resonance frequency higher than 32.768 kHz, whereincomprising the further steps of: forming metal films on the tuning forktines of the individual quartz crystal tuning fork resonators in thequartz crystal wafer by a spattering method or an evaporation method soas to get the individual quartz crystal tuning fork resonators each ofwhich has resonance frequency of 29.4 kHz to 32.75 kHz; mounting eachresonator at a mounting portion of a case; and adjusting the resonancefrequency of the each resonator by laser trimming or a plasma etchingmethod so that it is within a range of 32.764 kHz to 32.772 kHz when aquartz crystal unit comprising said quartz crystal tuning fork resonatoris provided, wherein said quartz crystal oscillating circuit comprisingthe amplification circuit and the feedback circuit is constructed sothat a ratio of an absolute value of negative resistance, |−RL₁| of afundamental mode vibration of the amplification circuit and seriesresistance R₁ of the fundamental mode vibration is larger than that ofan absolute value of negative resistance, |−RL₂| of a second overtonemode vibration of the amplification circuit and series resistance R₂ ofthe second overtone mode vibration, and an output signal of said quartzcrystal oscillating circuit is outputted through a buffer circuit andhas a frequency of 32.764 kHz to 32.772 kHz, and wherein comprising thefurther step of inspecting the individual quartz crystal tuning forkresonators formed in the quartz crystal wafer, and when there is afailure resonator therein, it is removed from the quartz crystal waferor something is marked on it or it is remembered by a computer.

[0017] The present invention will be more fully understood by referringto the following detailed specification and claims taken in connectionwith the appended drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018]FIG. 1 shows a general view of a flexural mode, quartz crystaltuning fork resonator embodying the present invention;

[0019]FIG. 2 shows a D-D′ cross-sectional view of the tuning fork baseof FIG. 1, and illustrating electrode construction;

[0020]FIG. 3 shows a plan view of a quartz crystal tuning fork resonatorof FIG. 1;

[0021]FIG. 4 shows a plan view of a flexural mode, quartz crystal tuningfork resonator embodying the present invention;

[0022]FIG. 5a and FIG. 5b show a plan view and a side view of a contourmode quartz crystal resonator capable of vibrating in awidth-extensional mode embodying the present invention;

[0023]FIG. 6 shows a cross-sectional view of a quartz crystal unitembodying the present invention, and in which a quartz crystal tuningfork resonator is housed;

[0024]FIG. 7 shows a step diagram of a method for manufacturing a quartzcrystal tuning fork resonator and a quartz crystal unit of the presentinvention;

[0025]FIG. 8 shows a diagram of an embodiment of a quartz crystaloscillating circuit which constructs a quartz crystal oscillator of thepresent invention;

[0026]FIG. 9 shows a diagram of the feedback circuit of FIG. 8;

[0027]FIG. 10 shows a cross-sectional view of a quartz crystaloscillator embodying the present invention.

DETAILED DESCRIPTION

[0028] Referring now to the drawings, the embodiments of the presentinvention will be described in more detail.

[0029]FIG. 1 shows a general view of a flexural mode, quartz crystaltuning fork resonator 10 embodying the present invention and itscoordinate system o-xyz. A cut angle θ, which has a typical value of 0°to 10°, is rotated from a Z-plate perpendicular to the z axis about thex axis. The quartz crystal resonator 10 comprises two tuning fork tines20 and 26 and a tuning fork base 40. The tines 20 and 26 have grooves 21and 27 respectively, with the grooves 21 and 27 extending into the base40. In addition, the base 40 has the additional grooves 32 and 36.

[0030]FIG. 2 shows a D-D′ cross-sectional view of the tuning fork base40 for the quartz crystal resonator 10 of FIG. 1. In FIG. 2, the shapeof the electrode construction within the base 40 for the quartz crystalresonator of FIG. 1 is described in detail. The section of the base 40which couples to the tine 20 has the grooves 21 and 22 cut into theobverse and reverse faces of the base 40. Also, the section of the base40 which couples to the tine 26 has the grooves 27 and 28 cut into theobverse and reverse faces of the base 40. In addition to these grooves,the base 40 has the grooves 32 and 36 cut between the grooves 21 and 27,and also, the base 40 has the grooves 33 and 37 cut between the grooves22 and 28.

[0031] Furthermore, the grooves 21 and 22 have the first electrodes 23and 24 both of the same electrical polarity, the grooves 32 and 33 havethe second electrodes 34 and 35 both of the same electrical polarity,the grooves 36 and 37 have the third electrodes 38 and 39 both of thesame electrical polarity, the grooves 27 and 28 have the fourthelectrodes 29 and 30 both of same electrical polarity and the sides ofthe base 40 have the fifth and sixth electrodes 25 and 31, each ofopposite electrical polarity. In more detail, the fifth, fourth, andsecond electrodes 25, 29, 30, 34 and 35 have the same electricalpolarity, while the first, sixth and third electrodes 23, 24, 31, 38 and39 have the opposite electrical polarity to the others. Two electrodeterminals E-E′ are constructed. That is, the electrodes disposed insidethe grooves constructed opposite each other in the thickness (z axis)direction have the same electrical polarity. Also, the electrodesdisposed opposite each other across adjoining grooves have oppositeelectrical polarity.

[0032] In addition, the resonator has a thickness t of the tuning forktines or the tuning fork tines and the tuning fork base, and a groovethickness t₁. It is needless to say that the electrodes are disposedinside the grooves and on the sides of the tuning fork tines. In thisembodiment, the first electrodes 23 and 24 are disposed at the tine andthe base, and also, the fourth electrodes 29 and 30 are disposed at thetine and the base. In addition, the electrodes are disposed on the sidesof the tines opposite each other to the electrodes disposed inside thegrooves. Namely, the electrodes are disposed opposite each other insidethe grooves and on the sides of the tuning fork tines so that theelectrodes disposed opposite each other are of opposite electricalpolarity and the tuning fork tines are capable of vibrating in inversephase.

[0033] Now, when a direct current (DC) voltage is applied between theelectrode terminals E-E′ (E terminal: plus, E′ terminal: minus), anelectric field Ex occurs in the arrow direction as shown in FIG. 2. Asthe electric field Ex occurs perpendicular to the electrodes disposed onthe base and the tines, the electric field Ex has a very large value anda large distortion occurs at the base and the tines, so that a flexuralmode, quartz crystal tuning fork resonator is obtained with a smallseries resistance R₁ and a high quality factor Q₁, even if it isminiaturized.

[0034]FIG. 3 shows a plan view of the resonator 10 of FIG. 1. In FIG. 3,the construction and the dimension of grooves 21, 27, 32 and 36 aredescribed in detail. The groove 21 is constructed to include a portionof the central line 41 of the tine 20, the groove 27 is similarlyconstructed to include a portion of the central line 42 of the tine 26.The width W₂ of the grooves 21 and 27 (groove width W₂) which include aportion of the central lines 41 and 42 respectively, is preferablebecause moment of inertia of the tines 20 and 26 becomes large and thetines can vibrate in a flexural mode very easily. As a result of whichthe flexural mode, tuning fork, quartz crystal resonator capable ofvibrating in a fundamental mode can be obtained with a small seriesresistance R₁ and a high quality factor Q₁.

[0035] In more detail, when part widths W₁, W₃ and groove width W₂ aretaken, the tine width W of the tines 20 and 26 has a relationship ofW=W₁+W₂+W₃, and a part or all of at least one of the grooves isconstructed so that W₁≧W₃ or W₁<W₃. In addition, the groove width W₂ isconstructed so that W₂≧W₁, W₃. In this embodiment, also, the grooves areconstructed at the tuning fork tines so that a ratio(W₂/W) of the groovewidth W₂ and the tine width W is larger than 0.35 and less than 1, and aratio(t₁/t) of the groove thickness t₁ and the thickness t of the tuningfork tines (tine thickness t) is less than 0.79, preferably, within arange of 0.01 to 0.79 to obtain very large moment of inertia of thetuning fork tines. That is to say, the flexural mode, quartz crystaltuning fork resonator, capable of vibrating in the fundamental mode, andhaving a high frequency stability can be provided with a small seriesresistance R₁, a high quality factor Q₁ and a small capacitance ratio r₁because electromechanical transformation efficiency of the resonatorbecomes large markedly.

[0036] Likewise, length l₁ of the grooves 21 and 27 of the tines 20 and26 extends into the base 40 in this embodiment (which has a dimension ofthe length l₂ and the length l₃ of the grooves). Therefore, groovelength and length of the tuning fork tines are given by (l₁-l₃) and(l-l₂), respectively, and a ratio of (l₁-l₃) and (l-l₂) is within arange of 0.4 to 0.8 to get a flexural mode, quartz crystal tuning forkresonator with series resistance R₁ of a fundamental mode vibrationsmaller than series resistance R₂ of a second overtone mode vibration

[0037] Furthermore, the total length l is determined by the frequencyrequirement and the size of the housing case. At the same time, to get aflexural mode, quartz crystal tuning fork resonator capable of vibratingeasily in a fundamental mode with suppression of the second overtonemode vibration which is unwanted mode vibration, there is a closerelationship between the groove length l₁ and the total length l.Namely, a ratio(l₁/l) of the groove length l₁ and the total length l iswithin a range of 0.2 to 0.78 because the quantity of charges whichgenerate within the grooves and on the sides of the tuning fork tines orthe tuning fork tines and the tuning fork base can be controlled by theratio, as a result, the second overtone mode vibration can be suppressedsubstantially, and simultaneously, a frequency stability of thefundamental mode vibration gets high. Therefore, the flexural mode,quartz crystal tuning fork resonator, capable of vibrating easily in thefundamental mode and having the high frequency stability can beprovided.

[0038] In more detail, series resistance R₁ of the fundamental modevibration becomes smaller than series resistance R₂ of the secondovertone mode vibration. Namely, R₁<R₂, preferably, R₁<0.86R₂,therefore, a quartz crystal oscillator (oscillator circuit) comprisingan amplifier (CMOS inverter), capacitors, resistors(resistance elements)and a quartz crystal unit with the quartz crystal tuning fork resonatorof this embodiment can be obtained, which is capable of vibrating in thefundamental mode very easily. In addition, in this embodiment thegrooves 21 and 27 of the tines 20 and 26 extend into the base 40 inseries, but embodiment of the present invention includes a plurality ofgrooves divided into the length direction of the tuning fork tines. Inaddition, the grooves may be constructed only at the tuning forktines(l₃=0), as will be shown in FIG. 4.

[0039] In this embodiment, the groove length l₁ corresponds to electrodelength disposed inside the grooves, though the electrode is not shown inFIG. 3, but, when the electrode length is less than the groove length,the length l₁ is of the electrode length. Namely, the ratio(l₁/l) inthis case is expressed by a ratio of electrode length l₁ of the groovesand the total length l. Also, a fork portion of this embodiment has arectangular shape, but this invention is not limited to this, forexample, the fork portion may have a U shape.

[0040] In addition, a space of between the tuning fork tines is given byW₄, and in this embodiment, the space W₄ and the groove width W₂ areconstructed so that W₄≧W₂, and more, the space W₄ is within a range of0.05 mm to 0.35 mm and the width W₂ is within a range of 0.02 mm to0.068 mm because it is easy to form a tuning fork shape and grooves ofthe tuning fork tines separately by a photo-lithographic process and anetching process, as a result, a frequency stability for a fundamentalmode vibration gets higher than that for a second overtone modevibration. In this embodiment, a quartz crystal wafer with the thicknesst of 0.05 mm to 0.12 mm is used. But, it is possible to use the waferthicker than 0.12 mm.

[0041] In more detail, to obtain a flexural mode, quartz crystal tuningfork resonator with a high frequency stability which gives high timeaccuracy, it is necessary to obtain the resonator whose resonancefrequency is not influenced by shunt capacitance because quartz crystalis a piezoelectric material and the frequency stability is verydependent on the shunt capacitance. In order to decrease the influenceon the resonance frequency by the shunt capacitance, figure of meritM_(i) plays an important role. Namely, the figure of merit M_(i) thatexpresses inductive characteristics, electromechanical transformationefficiency and a quality factor of a flexural mode, quartz crystaltuning fork resonator, is defined by a ratio (Q_(i)/r_(i)) of a qualityfactor Q_(i) and capacitance ratio r_(I,) namely, M_(i) is given byM_(i)=Q_(i)/r_(i,) where i shows vibration order of a quartz crystaltuning fork resonator, and for example, when i=1 and 2, figures of meritM₁ and M₂ are for a fundamental mode vibration and a second overtonemode vibration, respectively.

[0042] Also, a frequency difference Δf of resonance frequency f_(s) ofmechanical series independent on the shunt capacitance and resonancefrequency f_(r) dependent on the shunt capacitance is inverselyproportional to the figure of merit M_(i). The larger the value M_(i)becomes, the smaller the difference Δf becomes. Namely, the influence onthe resonance frequency f_(r) by the shunt capacitance decreases becauseit is close to the resonance frequency f_(s). Accordingly, the largerthe M_(i) becomes, the higher the frequency stability of the flexuralmode, quartz crystal tuning fork resonator becomes because the resonancefrequency f_(r) of the resonator is almost never dependent on the shuntcapacitance whose value changes with time. Namely, the flexural mode,quartz crystal tuning fork resonator can be provided with a high timeaccuracy.

[0043] In detail, a quartz crystal tuning fork resonator capable ofvibrating in a flexural mode can be obtained with figure of merit M₁ ofa fundamental mode vibration larger than figure of merit M₂ of a secondovertone mode vibration by the above-described tuning fork shape,grooves and dimensions. That is to say, M₁>M₂. As an example, whenresonance frequency of a quartz crystal tuning fork resonator is about32.768 kHz for a fundamental mode vibration and the resonator has avalue of W₂/W=0.5, t₁/t=0.34 and l₁/l=0.48, though there is adistribution in production, the quartz crystal tuning fork resonator hasa value of M₁>65 and M₂<30, respectively.

[0044] Namely, the flexural mode, quartz crystal tuning fork resonatorwhich is capable of vibrating in the fundamental mode can be providedwith high inductive characteristics, good electromechanicaltransformation efficiency (small capacitance ratio r₁ and small seriesresistance R₁) and a high quality factor. As a result, a frequencystability of the fundamental mode vibration becomes higher than that ofthe second overtone mode vibration, and simultaneously, the secondovertone mode vibration can be suppressed because capacitance ratio r₂and series resistance R₂ of the second overtone mode vibration becomelarger than capacitance ratio r₁ and series resistance R₁ of thefundamental mode vibration, respectively.

[0045] Therefore, the resonator capable of vibrating in the fundamentalmode vibration can be provided with a high time accuracy because it hasthe high frequency stability. Consequently, a quartz crystal oscillatingcircuit comprising the flexural mode, quartz crystal tuning forkresonator of this embodiment outputs a frequency of the fundamental modevibration as an output signal, and the frequency of the output signalhas a very high stability, namely, an excellent time accuracy. In otherwords, the quartz crystal oscillator of this embodiment has a remarkableeffect such that a frequency change by ageing becomes very small. Also,a frequency of a fundamental mode vibration of the present invention isless than 200 kHz, preferably, within a range of 10 kHz to 200 kHz.Especially, 32.768 kHz is used widely.

[0046] In addition, groove length l₁ of the present invention is lengthof grooves constructed at tuning fork tines so that the ratio(t₁/t) ofthe groove thickness t₁ and the tine thickness t is less than 0.79, andthe ratio(W₂/W) of the groove width W₂ and the tine width W is largerthan 0.35 and less than 1, when the grooves are constructed only at thetuning fork tines, and also, when the grooves constructed at the tuningfork tines extend into a tuning fork base and at least one groove isconstructed between the grooves extended into the tuning fork base,groove length l₁ of the present invention is length of groovesconstructed at the tuning fork tines and the tuning fork base(groovelength l₃).

[0047] Namely, when the grooves constructed at the tuning fork tinesextend into the tuning fork base and at least one groove is notconstructed between the grooves extended into the tuning fork base, thegroove length l₁ of the present invention is length of groovesconstructed at the tuning fork tines. Also, when the grooves of thetines are divided into the length direction thereof or connected via atleast one step portion, the groove length l₁ is total length of thelength direction satisfying the ratios(t₁/t) and (W₂/W) described above.In addition, the groove thickness t₁ of the present invention is thethinnest thickness of the grooves because quartz crystal is ananisotropic material and the groove thickness t₁ has a distribution whenit is formed by a chemical etching method.

[0048]FIG. 4 shows a plan view of a flexural mode, quartz crystal tuningfork resonator 45 embodying the present invention. The resonator 45comprises tuning fork tines 46, 47 and a tuning fork base 48. The tines46, 47 and the base 48 are formed integrally by a chemical etchingprocess. In this embodiment, the base 48 has cut portions 53 and 54.Also, a groove 49 is constructed to include a portion of the centralline 51 of the tine 46, a groove 50 is similarly constructed to includea portion of the central line 52 of the tine 47. In this embodiment, thegrooves 49 and 50 are constructed at a part of the tines 46 and 47, andhave groove width W₂ and groove length l₁.

[0049] In this embodiment, though electrodes are not shown in FIG. 4,the electrodes are disposed inside the grooves 49, 50 and on sides ofthe tuning fork tines 46 and 47, similar to FIG. 2. In detail, theelectrodes are disposed opposite each other inside the grooves and onthe sides of the tuning fork tines so that the electrodes disposedopposite each other are of opposite electrical polarity and the tuningfork tines are capable of vibrating in inverse phase.

[0050] Also, in this embodiment, the width W₂ of the grooves 49 and 50(groove width W₂) which include a portion of the central lines 51 and52, respectively, is preferable because moment of inertia of the tines46 and 47 becomes large and the tines are capable of vibrating in aflexural mode very easily. Also, though grooves of reverse face of thetines are not shown in FIG. 4, the grooves are constructed opposite eachother to the grooves 49 and 50 at the reverse face of the tines 46 and47, and electrodes are disposed inside the grooves and on sides of thetines, similar to FIG. 2.

[0051] In addition, the base 48 has cut portions 53 and 54, and the cutbase 48 has a dimension of width W₅ (tines side) and width W₆ (oppositeside to the tines side). When the base 48 is mounted at a mountingportion of a case of surface mounting type or tubular type by solder orconductive adhesives, it is necessary to satisfy W₆≧W₅ to decreaseenergy losses by vibration. The cut portions 53 and 54 are veryeffective to decrease the energy losses. Therefore, the flexural mode,quartz crystal tuning fork resonator, capable of vibrating in thefundamental mode and having the high frequency stability (high timeaccuracy) can be provided with a small series resistance R₁ and a highquality factor Q₁. Also, the width dimensions W=W₁+W₂+W₃ and W₄, andthe. length dimensions l₁, l₂ and l are as already described in relationto FIG. 3.

[0052]FIG. 5a and FIG. 5b are a plan view and a side view of a contourmode quartz crystal resonator capable of vibrating in awidth-extensional mode embodying the present invention, so called awidth-extensional mode quartz crystal resonator 62. The resonator 62comprises vibrational portion 63, connecting portions 66, 69 andsupporting portions 67, 80 including respective mounting portions 68,81. In addition, the supporting portions 67 and 80 have respective-holes67 a and 80 a. Also, electrodes 64 and 65 are disposed opposite eachother on upper and lower faces of the vibrational portion 63, theelectrodes have opposite electrical polarities. Namely, a pair ofelectrodes is disposed on the vibrational portion. In this case, afundamental mode vibration can be excited easily.

[0053] In addition, the electrode 64 extends to the mounting portion 81through the one connecting portion 69 and the electrode 65 extends tothe mounting portion 68 through the other connecting portion 66. In thisembodiment, the electrodes 64 and 65 disposed on the vibrational portion63 extend to the mounting portions of the different direction eachother. However, a resonator with the same characteristics as saidresonator can be obtained, even if the electrodes 64 and 65 extend tothe mounting portions of the same direction each other. The resonator inthis embodiment is mounted on fixing portions of a case or a lid at themounting portions 68 and 81 by conductive adhesives or solder.

[0054] With respect to a cutting angle of the width-extensional modequartz crystal resonator, it is shown here. First, a quartz crystalplate perpendicular to x axis, so called, X plate quartz crystal istaken. Width W₀, length L₀ and thickness T₀ which are each dimension ofthe X plate quartz crystal correspond to the respective directions of y, z and x axes.

[0055] Next, this X plate quartz crystal is, first, rotated with anangle θ_(x) of −25° to +25° about the x axis, and second, rotated withan angle θ_(y) of −30° to +30° about y′ axis which is the new axis ofthe y axis. In this case, the new axis of the x axis changes to x′ axisand the new axis of the z axis changes to z″ axis because the z axis isrotated twice about two axes. the width-extensional mode quartz crystalresonator of the present invention is formed from the quartz crystalplate with the rotation angles.

[0056] In other words, according to an expression of IEEE notation, acutting angle of the width-extensional mode quartz crystal resonator ofthe present invention can be expressed by XZtw(−25°-+25°)/(−30°-+30°).Also, when a turn over temperature point T_(p) is taken in a vicinity ofroom temperature, a cutting angle of the quartz crystal resonator may bewithin a range of XZt(−12°-−13.5°) or XZt(−18.5°-−19.8°) orXZtw(−13°-−18°)/±(+0.5°-+30°). Namely, said three kinds of cuttingangles in this embodiment is in the same direction as the cutting angleof the DT cut quartz crystal resonator, which is formed from a rotatedY-plate about the x axis whose Y-plate is perpendicular to the y axis.

[0057] Moreover, the vibrational portion 63 has a dimension of width W₀,length L₀ and thickness Z₀, also, width W₀, length L₀ and thickness T₀correspond to y′, z″ and x′ axes, respectively. That is, the electrodes64 and 65 are disposed on the upper and lower faces of the vibrationalportion 63 perpendicular to the x′ axis.

[0058] In addition, the vibrational portion 63 has a dimension of lengthL₀ greater than width W₀ and thickness T₀ smaller than the width W₀.Namely, a coupling between a width-extensional mode and alength-extensional mode gets so small as it can be ignored, as a resultof which, the quartz crystal resonator can vibrate in a singlewidth-extensional mode, and also, a width-to-length ratio (W₀/L₀) has avalue smaller than 0.7 to provide the resonator with a small seriesresistance R₁ by increasing electrode area of the vibrational portion.In addition, a thickness-to-width ratio (T₀/W₀) has a value smaller than0.85 to provide the resonator with a small R₁ by increasing theintensity of an electric field E_(x), These actual dimensions are,therefore, determined by the requirement characteristics for thewidth-extensional mode quartz crystal resonator.

[0059] In more detail, resonance frequency of the width-extensional modequartz crystal resonator is inversely proportional to width W₀, and itis almost independent on such an other dimension as length L₀, thicknessT₀, connecting portions and supporting potions. Also, in order to obtaina width-extensional mode quartz crystal resonator with a frequency of 4MHz, the width W₀ is about 0.7 mm. Thus, the miniature width-extensionalmode quartz crystal resonator can be provided with a frequency less than135 MHz, preferably, within a range of 1 MHz to 135 MHz becauseresonance frequency of the resonator is inversely proportional to thewidth W₀. Also, the resonator capable of vibrating in a singlewidth-extensional mode can be obtained from the relation of saiddimensions.

[0060] Consequently, a quartz crystal oscillator comprising a quartzcrystal oscillating circuit comprising the resonator of this embodimenthaving a high electromechanical transformation efficiency can beprovided with a small series resistance R₁ and a high quality factor Q.Also, the quartz crystal oscillating circuit comprises an amplificationcircuit comprising an amplifier at least and a feedback circuitcomprising the quartz crystal resonator and capacitors at least. Indetail, the amplification circuit comprises a CMOS inverter and afeedback resistor and the feedback circuit comprises a drain resistor,the resonator, a capacitor of a gate side and a capacitor of a drainside. Therefore, an output signal of the quartz crystal oscillator ofthis embodiment is used as a clock signal.

[0061] Now, when an alternating current (AC) voltage is applied betweenthe electrodes 64 and 65 shown in FIG. 5b, an electric field E_(x)occurs alternately in the thickness direction, as shown by the arrowdirection of the solid and broken lines. Consequently, the vibrationalportion 63 is capable of extending and contracting in the widthdirection. In this embodiment, though the width-extensional mode quartzcrystal resonator is described in detail, which is one of a contour modequartz crystal resonator, this invention is not limited to this, butincludes a length-extensional mode quartz crystal resonator and a Lamemode quartz crystal resonator, each of which is capable of vibrating ina contour mode, and has a vibrational portion, connecting portions andsupporting portions respectively.

[0062] Especially, for the Lame mode quartz crystal resonator, thevibrational portion and the supporting portions are connected at cornersof the vibrational portion through the connecting portions andelectrodes are disposed opposite each other on upper and lower faces ofthe vibrational portion so that the electrodes opposite each other areof opposite electrical polarity. Also, the length-extensional modequartz crystal resonator of the present invention can be obtained byreplacing the width with the length and the length with the width of thewidth-extensional mode quartz crystal resonator. Therefore, theconnecting portions and the supporting portions are constructed in thewidth direction and the connecting portions are connected at ends of thevibrational portion.

[0063]FIG. 6 shows a cross-sectional view of a quartz crystal unitembodying the present invention. In this embodiment, the quartz crystalunit 170 comprises a flexural mode, quartz crystal tuning fork resonator70, a case 71 and a lid 72. In more detail, the resonator 70 is mountedat a mounting portion 74 of the case 71 by conductive adhesives 76 orsolder. Also, the case 71 and the lid 72 are connected through aconnecting member 73. The resonator 70 in this embodiment is the sameresonator as one of the flexural mode, quartz crystal tuning forkresonators 10 and 45 described in detail in FIG. 1-FIG. 4. Also, in thisembodiment, circuit elements are connected at outside of the quartzcrystal unit to get a quartz crystal oscillator. Namely, only the quartzcrystal tuning fork resonator is housed in the unit (package) and also,it is housed in the unit in vacuum. In this embodiment, the quartzcrystal unit of surface mounting type is shown, but the quartz crystaltuning fork resonator may be housed in a unit of tubular type. Forexample, when a quartz crystal tuning fork resonator is housed in theunit of tubular type, a case has two lead wires as a mounting portionand the resonator is mounted on the two lead wires. This is called aquartz crystal unit of tubular type.

[0064] In this embodiment, the quartz crystal unit comprises theflexural mode, quartz crystal tuning fork resonator, but may comprisethe length-extensional mode quartz crystal resonator or the Lame modequartz crystal resonator described above in detail, instead of thetuning fork resonator.

[0065] In addition, a member of the case and the lid is ceramics orglass and a metal or glass, respectively, and a connecting member is ametal or glass with low melting point. Also, a relationship of theresonator, the case and the lid described in this embodiment is appliedto a quartz crystal oscillator of the present invention which will bedescribed in FIG. 10

[0066] Next, a method for manufacturing a quartz crystal resonator, aquartz crystal unit and a quartz crystal oscillator of the presentinvention is described in detail, according to the manufacturing steps.

[0067]FIG. 7 shows an embodiment of a method for manufacturing a quartzcrystal resonator, a quartz crystal unit and a quartz crystal oscillatorof the present invention and a step diagram embodying the presentinvention. In this embodiment, a quartz crystal tuning fork resonatorcapable of vibrating in a flexural mode is described. The signs of S-1to S-12 are the step numbers. First, S-1 shows a cross-sectional view ofa quartz crystal wafer 140. Next, in S-2 metal film 141, for example,chromium and gold on the chromium are, respectively, disposed on upperand lower faces of the quartz crystal wafer 140 by an evaporation methodor a spattering method. In addition, resist 142 is spread on said metalfilm 141 in S-3, and after the metal film 141 and the resist 142 wereremoved except those of tuning fork shape by a photo-lithographicprocess and an etching process, the tuning fork shape having tuning forktines 143, 144 and a tuning fork base 145, as be shown in S-4, isintegrally formed by a chemical etching process. In S-4, the resist andthe metal film disposed on the tuning fork shape are removed after itwas formed. When the tuning fork shape is formed, cut portions may beformed at the tuning fork base. In FIG. 7 the formation of a piece oftuning fork shape is shown, but, a plurality of individual tuning forkshapes are actually formed in a quartz crystal wafer.

[0068] Similar to the steps of S-2 and S-3, metal film and resist arespread again on the tuning fork shape of S-4 and grooves 146, 147, 148and 149 each of which has two step difference portions along the lengthdirection of the tuning fork tines, are formed at the tuning fork tines143, 144 by a photo-lithographic process and an etching process, and theshape of S-5 is obtained after all of the resist and the metal film wereremoved. In addition, metal film and resist are spread again on theshape of S-5 and electrodes which are of opposite electrical polarity,are disposed opposite each other on sides of the tuning fork tines andinside the grooves thereof, as be shown in S-6.

[0069] Namely, electrodes 150, 153 disposed on the sides of the tuningfork tine 143 and electrodes 155, 156 disposed inside the grooves 148,149 of the tuning fork tine 144 have the same electrical polarity.Similarly, electrodes 151, 152 disposed inside the grooves 146, 147 ofthe tuning fork tine 143 and electrodes 154, 157 disposed on the sidesof the tuning fork tine 144 have the same electrical polarity. Twoelectrode terminals are, therefore, constructed. In more detail, when analternating current (AC) voltage is applied between the terminals, thetuning fork tines are capable of vibrating in a flexural mode of inversephase because said electrodes disposed on step difference portions ofthe grooves and the electrodes disposed opposite to the said electrodeshave opposite electrical polarity. In the step of S-6, a piece offlexural mode, quartz crystal tuning fork resonator capable of vibratingin a fundamental mode is shown in the quartz crystal wafer, but aplurality of individual quartz crystal tuning fork resonators, each ofwhich comprises tuning fork tines and a tuning fork base capable ofvibrating in a flexural mode and has resonance frequency higher than32.768 kHz in the fundamental mode vibration, are actually formed in thequartz crystal wafer.

[0070] Next, metal films are formed on the tuning fork tines of theindividual quartz crystal tuning fork resonators in the quartz crystalwafer by a spattering method or an evaporation method so as to get theindividual quartz crystal tuning fork resonators each of which hasresonance frequency lower than 32.768 kHz, preferably, within a range of29.4 kHz to 32.75 kHz.

[0071] In addition, resonance frequency for the individual resonators isadjusted by a separate step of at least twice and the first adjustmentof resonance frequency for the individual resonators is performed in thequartz crystal wafer by laser trimming or a plasma etching method sothat the resonance frequency of the individual resonators is within arange of 32.2 kHz to 33.08 kHz. The adjustment of frequency by lasertrimming or a plasma etching method is performed by trimming the metalfilms disposed on the tuning fork tines to increase the resonancefrequency, on the other hand, the adjustment of frequency by anevaporation method is performed by adding mass such as a metal on tuningfork tines to decrease the resonance frequency. Namely, those methodscan change the resonance frequency of the resonators. Also, theindividual resonators formed in the quartz crystal wafer are inspectedtherein and when there is a failure resonator, it is removed from thequartz crystal wafer or something is marked on it or it is remembered bya computer.

[0072] In this embodiment, the tuning fork shape is formed from the stepof S-3 and after that, the grooves are formed at the tuning fork tines,namely, the tuning fork tines are formed before the grooves are formed,but this invention is not limited to said embodiment, for example, thegrooves are first formed from the step of S-3 and after that, the tuningfork shape may be formed, namely, the grooves are formed before thetuning fork tines are formed. Also, the tuning fork shape and thegrooves may be formed simultaneously, namely, the tuning fork tines andthe grooves are formed simultaneously. In addition, the grooves each ofwhich has two step difference portions along the direction of length ofthe tuning fork tines, are formed in this embodiment, but, each of thegrooves may have step difference portions more than two along the lengthdirection of the tines, at least two of which are connected via at leastone step portion.

[0073] Also, in this embodiment, though the grooves are constructed atthe tuning fork tines and the electrodes are disposed inside thegrooves, this invention is not limited to this, namely, the grooves maynot be constructed at the tuning fork tines. In more detail, the tuningfork tines have obverse and reverse faces and sides and electrodes aredisposed on the obverse and reverse faces and the sides of the tines. Inaddition, electrodes disposed on obverse and reverse faces of tuningfork tines of the present invention implies electrodes disposed on theobverse and reverse faces of the tuning fork tines, notwithstandingthere is a groove at the tines or not. Therefore, it is needless to saythat this invention includes at least one connecting electrode disposedon at least one face of the obverse and reverse faces of the tines toconnect two electrodes. As a result of which the tuning fork tines arecapable of vibrating in inverse phase.

[0074] There are two methods of A and B in the following step, as beshown by arrow signs. For the step of A, the tuning fork base 145 of theformed flexural mode, quartz crystal tuning fork resonator 160 is firstmounted on mounting portion 159 of a case 158 by conductive adhesives161 or solder, as be shown in S-7. Next, the second adjustment ofresonance frequency for the resonator 160 is performed by laser 162 oran evaporation method or a plasma etching method in S-8 so that theresonance frequency is within a range of 32.764 kHz to 32.772 kHz whenthe resonator is housed in a package, namely, the quartz crystal unit isprovided. Finally, the case 158 and a lid 163 are connected via glass164 with the low melting point or a metal in S-9. In this case, theconnection of the case and the lid is performed in vacuum because thecase 158 has no hole to close it in vacuum.

[0075] In this embodiment, though the metal films are formed on thetuning fork tines of the individual quartz crystal resonators formed inthe quartz crystal wafer and resonance frequency of the individualresonators is adjusted therein by removing a part or all of the metalfilms by laser trimming or a plasma etching method, the presentinvention is not limited to this, namely, said steps may be omitted. Inmore detail, each of the individual resonators having resonancefrequency higher than 32.768 kHz is mounted at a mounting portion of acase and after that, the resonance frequency is adjusted by anevaporation method so that it is within a range of 32.764 kHz to 32.772kHz when a quartz crystal unit is provided.

[0076] In addition, though it is not visible in FIG. 7, the thirdfrequency adjustment may be performed by laser trimming after the stepof the connection of S-9 to get a small frequency deviation when amaterial of the lid is glass. As a result of which it is possible to getthe resonator with the resonance frequency of 32.766 kHz to 32.77 kHz.Like this step, when the third frequency adjustment is performed, theresonance frequency of the resonators by the second frequency adjustmentis adjusted so that it is within a range of 32.736 kHz to 32.8 kHz.

[0077] For the step of B, the tuning fork base 145 of the formedresonator 160 is first mounted on mounting portion 159 of a case 165 byconductive adhesives 161 or solder in S-10, in addition, in S-11 thecase 165 and a lid 163 are connected by the same way as that of S-9, inmore detail, after the resonator was mounted on the mounting portion ofthe case or after the resonator was mounted at the mounting portion andthe case and the lid were connected, the second adjustment of resonancefrequency is performed so that the resonance frequency is within a rangeof 32.764 kHz to 32.772 kHz in vacuum, but, it may be within a widerrange, for example, 32.736 kHz to 32.8 kHz when the third frequencyadjustment as will be shown as follows, is performed. Finally, a hole167 constructed at the case 165 is closed in vacuum using such a metal166 as solder or glass with the low melting point in S-12.

[0078] Also, similar to the step of A, the third adjustment of resonancefrequency may be performed by laser trimming after the step of S-12 toget a small frequency deviation. As a result of which it is possible toget the resonator with the resonance frequency of 32.766 kHz to 32.77kHz. Thus, the resonance frequency of the resonators in the case of Aand B is finally within a range of 32.764 kHz to 32.772 kHz at most.Also, the second frequency adjustment may be performed after the caseand the lid were connected and after that, the hole is closed in vacuum.In addition, the hole is constructed at the case, but may be constructedat the lid. Also, the frequency adjustment of the present invention isperformed in vacuum or inert gas such as nitrogen gas or atmosphere, andthe values described above are values in vacuum.

[0079] Therefore, the quartz crystal tuning fork resonators each ofwhich is capable of vibrating in a flexural mode and the quartz crystalunits manufactured by the above-described method are miniaturized andrealized with a small series resistance R₁, a high quality factor Q₁ andlow price.

[0080] Moreover, in the above-described embodiment, though the firstfrequency adjustment of the resonators is performed in the quartzcrystal wafer and at the same time, when there is a failure resonator,something is marked on it or it is removed from the quartz crystalwafer, but the present invention is not limited to this, namely, thepresent invention may include the step to inspect the flexural mode,quartz crystal tuning fork resonators formed in the quartz crystal wafertherein, in other words, the step to inspect whether there is a failureresonator or not in the quartz crystal wafer. When there is the failureresonator in the wafer, it is removed from the wafer or something ismarked on it or it is remembered by a computer. By including the step,it can increase a manufacturing yield of the quartz crystal resonatorsbecause it is possible to find out the failure resonator in an earlystep and the failure resonator does not go to the next step. As a resultof which low priced flexural mode, quartz crystal tuning fork resonatorscan be provided with excellent electrical characteristics. In thisembodiment, the frequency adjustment is performed three times by aseparate step, but may be performed at least twice by a separate step.For example, the third frequency adjustment may be omitted.

[0081] In this embodiment, the frequency adjustment is performed by aseparate step of at least twice. However, when a plurality of individualquartz crystal tuning fork resonators, each of which has a resonancefrequency higher than 32.768 kHz, are formed in a quartz crystal waferand each resonator is mounted at a mounting portion of a case or a lid,resonance frequency is adjusted by an evaporation method of at leastonce so that it is within a range of 32.764 kHz to 32.772 kHz when aquartz crystal unit is provided.

[0082] Also, for the manufacturing method of this embodiment, the stepsof forming a plurality of individual quartz crystal tuning forkresonator having resonance frequency higher than 32.768 kHz by achemical etching method and changing the resonance frequency by formingmetal films on tuning fork tines of the individual resonators are notincluded in the frequency adjustment of the present invention.

[0083] In addition, in order to construct a quartz crystal oscillatorcomprising: a quartz crystal oscillating circuit comprising; anamplification circuit comprising an amplifier at least and a feedbackcircuit comprising a quartz crystal tuning fork resonator capable ofvibrating in a flexural mode, and capacitors at least, two electrodeterminals of the resonators are connected electrically to the amplifierand the capacitors at least. Namely, the quartz crystal oscillatingcircuit comprises the step of connecting electrically the quartz crystaltuning fork resonator, the amplifier and the capacitors at least, Inmore detail, the quartz crystal oscillating circuit is constructed andconnected electrically so that the amplification circuit comprises aCMOS inverter and a feedback resistor and the feedback circuit comprisesthe flexural mode, quartz crystal tuning fork resonator, the drainresistor, the capacitor of a gate side and the capacitor of a drainside. Also, the third frequency adjustment may be performed after thequartz crystal oscillating circuit was constructed.

[0084] Next, an embodiment of a method for manufacturing a quartzcrystal unit comprising a contour mode quartz crystal resonator such asa width-extensional mode quartz crystal resonator, a length-extensionalmode quartz crystal resonator and a Lame mode quartz crystal resonator,a case and a lid is described in detail, the contour mode quartz crystalresonator comprises the step of: utilizing a particle method or achemical etching method to form a resonator comprising; avibrational-portion; connecting portions located at ends of saidvibrational portion; supporting portions connected to the vibrationalportion through the connecting portions; and electrodes disposedopposite each other on upper and lower faces of the vibrational portionso that the electrodes disposed opposite each other are of oppositeelectrical polarity.

[0085] In addition, a plurality of individual quartz crystal resonatorseach of which is capable of vibrating in a contour mode and a singlemode, are formed in a quartz crystal wafer with resonance frequencyhigher than a nominal frequency, and metal films are formed on thevibrational portion in the quartz crystal wafer by a spattering methodor an evaporation method so as to get the individual quartz crystalresonators each of which has resonance frequency lower than the nominalfrequency.

[0086] Moreover, each of the individual quartz crystal resonators ishoused in a case, and the resonance frequency of each resonator isadjusted by removing a part or all of the metal films formed on thevibrational portion by laser trimming or a plasma etching method so thata frequency deviation is within a range of −100 PPM to +100 PPM to thenominal frequency. Namely, the resonator is housed in a package with thefrequency deviation.

[0087] In this embodiment, the metal films are formed on the vibrationalportion, but they may not be formed on the vibrational portion. In thiscase, a plurality of individual contour mode quartz crystal resonatorseach of which is capable of vibrating in a contour mode and a singlemode, are formed in a quartz crystal wafer with resonance frequencylower than a nominal frequency, and each of the individual quartzcrystal resonators is housed in a case, and the resonance frequency ofeach resonator is adjusted by removing a part of the electrodes formedon the vibrational portion by laser trimming or a plasma etching -methodso that a frequency deviation is within a range of −100 PPM to +100 PPMto the nominal frequency. Namely, the resonator is housed in a packagewith the frequency deviation.

[0088] As described above, the contour mode quartz crystal resonators inthe embodiment have such complicated shapes as comprise the vibrationalportion, the connecting portions and the supporting portions. Also, theresonators in this embodiment of the present invention are generallyprocessed by a chemical etching method, but, when the etching speedwhich is very dependent on a cutting angle is extremely slow, it is verydifficult and impossible to process the resonators by the chemicaletching method. In this case, the resonators in this embodiment of thepresent invention are, therefore, processed by a physical method or amechanical method, and the resonators are formed integrally by at leastone method.

[0089] Namely, particles with mass are collided with a quartz crystalplate covered by resist corresponding to the shape of resonators by thephysical or mechanical method, as a result of which, the shape of theresonators is processed because atoms or molecules of the quartz crystalplate scatter. This method is called “particle method” here. This methodis, substantially, different from the chemical etching method and at thesame time, it has a feature that the processing speed is also very fast.

[0090] According to this particle method, low priced quartz crystalresonators can be provided similar to the chemical etching methodbecause the processing time of outward shapes for the resonators shortenextremely. For this particle method, resist with elastic characteristicsis used to prevent the resist from defacement by particles, as theresist, for example, plastic resist for use in blast processing is wellknown. Also, for this particle method, for example, it is preferable touse particles of GC#1000 to GC#6000 or ion atoms or ion molecules as theparticles for use in processing. Especially, a method by ion etching iscalled “plasma etching method” in the present invention.

[0091] Additionally, an insulation material such as S_(i)O₂ may beconstructed on obverse and reverse faces of the width W₁ and the widthW₃ of the tuning fork tines to prevent a short circuit of between theelectrodes of the sides and the grooves thereof, and the insulationmaterial is formed by a spattering method or an evaporation method.Also, when a tuning fork shape comprising tuning fork tines and a tuningfork base is formed by a photo-lithographic process and an etchingprocess, cut portions may be also formed simultaneously at the tuningfork base.

[0092] Likewise, in the present embodiments the flexural mode quartzcrystal resonator of tuning fork type has two tuning fork tines, butembodiments of the present invention include tuning fork tines more thantwo. In addition, the quartz crystal tuning fork resonators of thepresent embodiments are housed in a package (unit) of surface mountingtype comprising a case and a lid, but may be housed in a package oftubular type.

[0093]FIG. 8 shows a diagram of an embodiment of a quartz crystaloscillating circuit constructing a quartz crystal oscillator of thepresent invention. In this embodiment, the quartz crystal oscillatingcircuit 1 comprises an amplifier (CMOS Inverter) 2, a feedback resistor4, drain resistor 7, capacitors 5, 6 and a flexural mode, quartz crystaltuning fork resonator 3. Namely, the quartz crystal oscillating circuit1 comprises an amplification circuit 8 having the amplifier 2 and thefeedback resistor 4, and a feedback circuit 9 having the drain resistor7, the capacitors 5, 6 and the flexural mode quartz crystal resonator 3.In addition, an output signal of the quartz crystal oscillating circuit1 comprising the flexural mode, quartz crystal tuning fork resonator 3,capable of vibrating in a fundamental mode, is outputted through abuffer circuit (not shown in FIG. 8) from a drain side of the amplifier(CMOS Inverter).

[0094] In detail, a frequency of the fundamental mode vibration isoutputted through a buffer circuit as an output signal. According to thepresent invention, a nominal frequency of the fundamental mode vibrationis 32.768 kHz. Also, the present invention includes a divided frequencyof the output signal having the frequency of 32.764 kHz to 32.772 kHz bya divided circuit. In more detail, the quartz crystal oscillator in thisembodiment comprises the quartz crystal oscillating circuit and thebuffer circuit, in other words, the quartz crystal oscillating circuitcomprises the amplification circuit and the feedback circuit, and theamplification circuit comprises the amplifier at least and the feedbackcircuit comprises the flexural mode, quartz crystal tuning forkresonator and the capacitors at least. Also, the quartz crystal tuningfork resonators each of which is capable of vibrating in a flexural modehave been already described in FIG. 1-FIG. 4 in detail.

[0095]FIG. 9 shows a diagram of the feedback circuit of FIG. 8. Now,when angular frequency ω_(i) of the flexural mode, quartz crystal tuningfork resonator 3, capable of vibrating in a flexural mode, a resistanceR_(d) of the drain resistor 7, capacitance C_(g), C_(d) of thecapacitors 5, 6, crystal impedance R_(ei) of the quartz crystalresonator 3, an input voltage V₁, and an output voltage V₂ are taken, afeedback rate β_(i) is defined by β_(i)=|V₂|_(i)/|V₁|_(i), where i showsvibration order, for example, when i=1 and 2, they are for fundamentalmode vibration and second overtone mode vibration, namely, when i=n, itis for n^(th) overtone mode vibration.

[0096] In addition, load capacitance C_(L) is given by C_(L)=C_(g)C_(d)/(C_(g)+C_(d)), and when C_(g)=C_(d)=C_(gd) and Rd>>R_(ei), thefeedback rate β_(i) is given by β_(i)=1/(1+kC_(L) ²), where k isexpressed by a function of ω_(i), R_(d) and R_(ei). Also, R_(ei) isapproximately equal to series resistance R_(i).

[0097] Thus, it is easily understood from a relationship of the feedbackrate β_(i) and load capacitance C_(L) that the feedback rate ofresonance frequency for a fundamental mode vibration and an overtonemode vibration becomes large, respectively, according to decrease ofload capacitance C_(L). Therefore, when CL has a small value, anoscillation of the overtone mode occurs very easily, instead of that ofthe fundamental mode. This is the reason why a maximum amplitude of theovertone mode vibration becomes smaller than that of the fundamentalmode vibration, and the oscillation of the overtone mode satisfies anamplitude condition and a phase condition simultaneously which are thecontinuous condition of an oscillation in an oscillating circuit.

[0098] In addition, in order to suppress a second overtone modevibration and to obtain a quartz crystal oscillator comprising a quartzcrystal oscillating circuit, comprising a flexural mode, quartz crystaltuning fork resonator and having an output signal of a frequency of afundamental mode vibration, the quartz crystal oscillating circuit inthis embodiment is constructed so that it satisfies a relationship ofα₁/α₂>β₂/β₁ and α₁β₁>1, where α₁ and α₂ are a amplification rate of thefundamental mode vibration and the second overtone mode vibration of anamplification circuit, and β₁ and β₂ are a feedback rate of thefundamental mode vibration and the second overtone mode vibration of afeedback circuit.

[0099] In other words, the quartz crystal oscillating circuit isconstructed so that a ratio of the amplification rate α₁ of thefundamental mode vibration and the amplification rate α₂ of the secondovertone mode vibration of the amplification circuit is larger than thatof the feedback rate β₂ of the second overtone mode vibration and thefeedback rate β₁ of the fundamental mode vibration of the feedbackcircuit, and a product of the amplification rate α₁ and the feedbackrate β₁ of the fundamental mode vibration is larger than 1. Byconstructing the oscillating circuit like this, it can be provided withreduced electric current consumption and the output signal of thefrequency of the fundamental mode vibration.

[0100] Also, characteristics of the amplifier of the amplificationcircuit constructing the quartz crystal oscillating circuit of thisembodiment can be expressed by negative resistance −RL_(i). For example,when i=1, negative resistance −RL₁ is for a fundamental mode vibrationand when i=2, negative resistance −RL₂ is for a second overtone modevibration. In this embodiment, the quartz crystal oscillating circuit isconstructed so that a ratio of an absolute value of negative resistance,|−RL₁| of the fundamental mode vibration of the amplification circuitand series resistance R₁ of the fundamental mode vibration is largerthan that of an absolute value of negative resistance, |−RL₂| of thesecond overtone mode vibration of the amplification circuit and seriesresistance R₂ of the second overtone mode vibration. That is to say, theoscillating circuit is constructed so that it satisfies a relationshipof |−RL₁|/R₁>|−RL₂|/R₂. By constructing the oscillating circuit likethis, an oscillation of the second overtone mode can be suppressed, as aresult of which an output signal of a frequency of the fundamental modevibration can be provided because an oscillation of the fundamental modegenerates easily in the oscillating circuit.

[0101]FIG. 10 shows a cross-sectional view of a quartz crystaloscillator embodying the present invention. The quartz crystaloscillator 190 comprises a quartz crystal oscillating circuit, a case 91and a lid 92. In this embodiment, circuit elements constructing theoscillating circuit are housed in a quartz crystal unit comprising aflexural mode, quartz crystal tuning fork resonator 90, the case 91 andthe lid 92. Also, the quartz crystal oscillating circuit of thisembodiment comprises an amplifier 98 including a feedback resistor, thequartz crystal tuning fork resonator 90, capacitors (not shown here) anda drain resistor (not shown here), and a CMOS inverter is used as theamplifier 98.

[0102] In addition, in this embodiment, the resonator 90 is mounted at amounting portion 94 of the case 91 by conductive adhesives 96 or solder.As described above, the amplifier 98 is housed in the quartz crystalunit and mounted at the case 91. Also, the case 91 and the lid 92 areconnected through a connecting member 93. The resonator 90 of thisembodiment is the same as one of the flexural mode, quartz crystaltuning fork resonators 10 and 45 described in detail in FIG. 1-FIG. 4.In this embodiment, though the resonator and the amplifier are housed inthe same room, the present invention is not limited to this, forexample, a room of the case is divided into two rooms by a dividedportion, and the amplifier is housed in one of the two rooms and theflexural mode, quartz crystal tuning fork resonator is housed in otherroom. Namely, the resonator and the amplifier are housed in a separateroom. Therefore, the quartz crystal oscillator of the present inventionalso includes that construction.

[0103] Likewise, in this embodiment, a piece of flexural mode, quartzcrystal tuning fork resonator is housed in the unit, but the presentinvention also includes a quartz crystal unit having a plurality ofindividual flexural mode, quartz crystal tuning fork resonators, and atleast two of the plurality of individual resonators are connectedelectrically in parallel. In detail, the at least two resonators may bean individual resonator or may be an individual resonator that is formedintegrally at each tuning base through a connecting portion.

[0104] The above-described resonators are formed by at least one methodof chemical, mechanical and physical etching methods. For example, thephysical etching method is a method by ion etching, so called “plasmaetching”.

[0105] In addition, for the flexural mode quartz crystal tuning forkresonators of the embodiments of the present invention, the resonatorsare provided so that a capacitance ratio r₁ of a fundamental modevibration gets smaller than a capacitance ratio r₂ of a second overtonemode vibration, in order to obtain a frequency change of the fundamentalmode vibration larger than that of the second overtone mode vibration,versus the same change of a value of load capacitance C_(L). Namely, avariable range of a frequency of the fundamental mode vibration getswider than that of the second overtone mode vibration. Also, C_(L) has avalue less than 18 pF to decrease electric current consumption in aquartz crystal oscillating circuit.

[0106] Moreover, capacitance ratios r₁ and r₂ of a flexural mode, quartzcrystal tuning fork resonator are given by r₁=C₀/C₁ and r₂=C₀/C₂,respectively, where C₀ is shunt capacitance in an electrical equivalentcircuit of the resonator, and C₁ and C₂ are, respectively, motionalcapacitance of a fundamental mode vibration and a second overtone modevibration in the electrical equivalent circuit of the resonator. Inaddition, the flexural mode, quartz crystal tuning fork resonator has aquality factor Q₁ for the fundamental mode vibration and a qualityfactor Q₂ for the second overtone mode vibration.

[0107] In detail, the tuning fork resonator of this embodiment isprovided so that the influence on resonance frequency of the fundamentalmode vibration by the shunt capacitance becomes smaller than that of thesecond overtone mode vibration by the shunt capacitance, namely, so thatit satisfies a relationship of r₁/2Q₁ ²<r₂/2Q₂ ². As a result, thetuning fork resonator, capable of vibrating in the fundamental mode andhaving a high frequency stability can be provided because the influenceon the resonance frequency of the fundamental mode vibration by theshunt capacitance becomes so extremely small as it can be ignored. Also,the present invention replaces r₁/2Q₁ ² with S₁ and r₂/2Q₂ ² with S₂,respectively, and here, S₁ and S₂ are called “stable factor offrequency” of the fundamental mode vibration and the second overtonemode vibration. Namely, S₁ and S₂ are given by S₁=r₁/2Q₁ ² and S₂=r₂/2Q₂², respectively.

[0108] In addition, when a power source is applied to the quartz crystaloscillating circuit, at least one oscillation which satisfies anamplitude condition and a phase condition of vibration starts in thecircuit, and a spent time to get to about ninety percent of the steadyamplitude of the vibration is called “rise time” here. Namely, theshorter the rise time becomes, the easier the oscillation becomes. Whenrise time t_(r1) of the fundamental mode vibration and rise time t_(r2)of the second overtone mode vibration in the circuit are taken, t_(r1)and t_(r2) are given by t_(r1)=kQ₁/(ω₁(−1+|−RL₁|/R₁)) andt_(r2)=kQ₂/(ω₂(−1+|−RL₂|/R₂)), respectively, where k is constant and ω₁and ω₂ are an angular frequency for the fundamental mode vibration andthe second overtone mode vibration, respectively.

[0109] From the above-described relation, it is possible to obtain therise time t_(r1) of the fundamental mode vibration less than the risetime t_(r2) of the second overtone mode vibration. As an example, whenresonance frequency of a flexural mode, quartz crystal tuning forkresonator is about 32.768 kHz for a fundamental mode vibration and theresonator has a value of W₂/W=0.5, t₁/t=0.34 and l₁/l=0.48, though thereis a distribution in production, as an example, the resonator has avalue of Q₁=62,000 and Q₂=192,000, respectively. In this embodiment, Q₂has a value of about three times of Q₁. Accordingly, to obtain thet_(r1) less than the t_(r2), it is necessary to satisfy a relationshipof |−RL₁|/R₁>2|−RL₂|/R₂−1 by using a relation of ω₂=6ω₁ approximately.

[0110] Also, according to this invention, the relationship is notlimited to the quartz crystal oscillating circuit comprising theresonator in this embodiment, but this invention includes all quartzcrystal oscillating circuits to satisfy the relationship. Byconstructing the oscillating circuit like this, a quartz crystaloscillator with the flexural mode, quartz crystal tuning fork resonatorcan be provided with a short rise time. In other words, an output signalof the oscillator has a frequency of a fundamental mode vibration of theresonator whose frequency is within a range of 32.764 kHz to 32.772 kHz,and is outputted through a buffer circuit. Namely, the second overtonemode vibration can be suppressed in the oscillating circuit. In thisembodiment, the resonator has also a value of r₁=320 and r₂=10,600 as anexample.

[0111] In addition, the contour mode quartz crystal resonators describedin the embodiments of the present invention, each of which is a flexuralmode, quartz crystal tuning fork resonator, a width-extensional modequartz crystal resonator, a length-extensional mode quartz crystalresonator and a Lame mode quartz crystal resonator, can be applied to anelectronic apparatus comprising a display portion and a quartz crystaloscillator at least such as cellar phone, telephone, TV set, camera,video set, video camera, pagers, personal computer, printer, CD player,MD player, electronic musical instrument, car navigator, carelectronics, timepiece, IC card and so forth.

[0112] In detail, the contour mode quartz crystal resonators each ofwhich constructs a quartz crystal oscillator comprising: a quartzcrystal oscillating circuit comprising; an amplification circuit and afeedback circuit as described above, are used as a clock signal of theelectronic apparatus. In more detail, an output signal of the quartzcrystal oscillating circuit comprising the quartz crystal tuning forkresonator capable of vibrating in a flexural mode has a frequency of32.764 kHz to 32.772 kHz and is outputted through a buffer circuit, andthe output signal is a clock signal which is used to display time at thedisplay portion of the electronic apparatus.

[0113] Likewise, an output signal of the quartz crystal oscillatingcircuit comprising a width-extensional mode quartz crystal resonator ora length-extensional mode quartz crystal resonator or a Lame mode quartzcrystal resonator is outputted through a buffer circuit, and the outputsignal is a clock signal which is used except time display of theelectronic apparatus.

[0114] In the present embodiments, the metal films for frequencyadjustment are formed on the tuning fork tines. As an example of thepresent invention, silver or gold is used as a material of the metalfilms and for example, the metal films are formed on at least two facesof obverse and reverse faces of the tuning fork tines. Preferably, theat least two faces are of the same faces.

[0115] As described above, it will be easily understood that the quartzcrystal resonators, the quartz crystal units and the quartz crystaloscillators of the present invention may have the outstanding effects.For example, the quartz crystal oscillator comprising: the quartzcrystal oscillating circuit comprising; the amplification circuit andthe feedback circuit having the flexural mode, quartz crystal tuningfork resonator, capable of vibrating in a fundamental mode and havingthe novel shapes, the novel electrode construction and good electricalcharacteristics, according to the present invention may have theoutstanding effects. In addition to this, while the present inventionhas been shown and described with reference to preferred embodimentsthereof, it will be understood by those skilled in the art that thechanges in shape and electrode construction can be made therein withoutdeparting from the spirit and scope of the present invention.

What is claimed is:
 1. A method for manufacturing a plurality ofindividual quartz crystal tuning fork resonators each of which iscapable of vibrating in a flexural mode, and each of the individualquartz crystal tuning fork resonators comprising the steps of: formingintegrally tuning fork tines each of which has a length, a width and athickness and the length greater than the width and the thickness, and atuning fork base; providing grooves; and disposing electrodes inside thegrooves and on sides of said tuning fork tines, and the grooves beingprovided at said tuning fork tines, and the electrodes being disposedopposite each other inside the grooves and on the sides of said tuningfork tines so that the electrodes disposed opposite each other are ofopposite electrical polarity and said tuning fork tines are capable ofvibrating in inverse phase, wherein the individual quartz crystal tuningfork resonators are provided in a quartz crystal wafer with resonancefrequency higher than 32.768 kHz, each of which is capable of vibratingin a fundamental mode, and next, metal films are formed on said tuningfork tines in the quartz crystal wafer by a spattering method or anevaporation method so as to get the individual quartz crystal tuningfork resonators each of which has resonance frequency lower than 32.768kHz, and wherein comprising the further steps of: adjusting theresonance frequency by removing a part or all of the metal films formedon said tuning fork tines in the quartz crystal wafer by laser trimmingor a plasma etching method; and inspecting the individual quartz crystaltuning fork resonators in the quartz crystal wafer, and when there is afailure resonator therein, it is removed from the quartz crystal waferor something is marked on it or it is remembered by a computer.
 2. Themethod of claim 1, wherein comprising the further step of forming saidtuning fork tines before the grooves are formed.
 3. The method of claim1, wherein comprising the further step of forming the grooves beforesaid tuning fork tines are formed.
 4. The method of claim 1, whereincomprising the further step of forming the grooves and said tuning forktines simultaneously.
 5. The method of claim 1, wherein the resonancefrequency lower than 32.768 kHz is within a range of 29.4 kHz to 32.75kHz.
 6. The method of claim 1, wherein the resonance frequency adjustedby the laser trimming or the plasma etching method is within a range of32.2 kHz to 33.08 kHz.
 7. The method of claim 1, wherein said groovesare through holes.
 8. The method of claim 5, wherein comprising thefurther step of housing each of the individual quartz crystal tuningfork resonators in a package of surface mounting type.
 9. The method ofclaim 5, wherein comprising the further step of housing each of theindividual quartz crystal tuning fork resonators in a package of tubulartype.
 10. A method for manufacturing a quartz crystal unit comprising acontour mode quartz crystal resonator which is one of awidth-extensional mode quartz crystal resonator, a length-extensionalmode quartz crystal resonator and a Lame mode quartz crystal resonator,a case and a lid, and said contour mode quartz crystal resonatorcomprising the step of: utilizing a particle method or a chemicaletching method to form a resonator comprising; a vibrational portion;connecting portions located at ends of said vibrational portion;supporting portions connected to said vibrational portion through saidconnecting portions; and electrodes disposed opposite each other onupper and lower faces of said vibrational portion so that the electrodesdisposed opposite each other are of opposite electrical polarity,wherein a plurality of individual contour mode quartz crystal resonatorsare formed in a quartz crystal wafer, each of which is capable ofvibrating in a contour mode and a single mode, and wherein each of saidindividual contour mode quartz crystal resonators is mounted at amounting portion of a case, and the resonance frequency of eachresonator is adjusted by laser trimming or a plasma etching method sothat a frequency deviation is within a range of −100 PPM to +100 PPM toa nominal frequency of less than 135 MHz when the quartz crystal unit isprovided.
 11. The method of claim 10, wherein comprising the furthersteps of providing said individual quartz crystal resonators withresonance frequency lower than the nominal frequency and adjusting theresonance frequency of each resonator by removing a part of theelectrodes formed on said vibrational portion by the laser trimming orthe plasma etching method.
 12. The method of claim 10, whereincomprising the further steps of forming said individual quartz crystalresonators in a quartz crystal wafer with resonance frequency higherthan the nominal frequency, forming metal films on said vibrationalportion in the quartz crystal wafer by a spattering method or anevaporation method so as to get said individual quartz crystalresonators each of which has resonance frequency lower than the nominalfrequency, and adjusting the resonance frequency of each resonator byremoving a part or all of the metal films formed on said vibrationalportion by the laser trimming or the plasma etching method
 13. A methodfor manufacturing a quartz crystal oscillator comprising: a quartzcrystal oscillating circuit comprising; an amplification circuitcomprising an amplifier at least and a feedback circuit comprising aquartz crystal tuning fork resonator and capacitors at least, saidquartz crystal tuning fork resonator comprising the steps of: formingintegrally tuning fork tines each of which has a length, a width and athickness and the length greater than the width and the thickness, and atuning fork base; providing grooves; and disposing electrodes inside thegrooves and on sides of said tuning fork tines, and the grooves beingprovided at said tuning fork tines, and the electrodes being disposedopposite each other inside the grooves and on the sides of said tuningfork tines so that the electrodes disposed opposite each other are ofopposite electrical polarity and said tuning fork tines are capable ofvibrating in inverse phase, and said quartz crystal oscillating circuitcomprising the step of connecting electrically said quartz crystaltuning fork resonator, the amplifier and the capacitors at least,wherein said quartz crystal tuning fork resonator is capable ofvibrating in a flexural mode and said quartz crystal oscillating circuitcomprises said quartz crystal tuning fork resonator whose figure ofmerit M₁ of a fundamental mode vibration is larger than figure of meritM₂ of a second overtone mode vibration to suppress the second overtonemode vibration and to get a high frequency stability for the fundamentalmode vibration.
 14. The method of claim 13, wherein said tuning forktines are formed before the grooves are formed.
 15. The method of claim13, wherein the grooves are formed before said tuning fork tines areformed.
 16. The method of claim 13, wherein the grooves and said tuningfork tines are formed simultaneously.
 17. The method of claim 13,wherein comprising the further step of constructing said quartz crystaloscillating circuit comprising a CMOS inverter, a feedback resistor,said quartz crystal tuning fork resonator capable of vibrating in aflexural mode, a drain resistor, a capacitor of a gate side and acapacitor of a drain side.
 18. The method of claim 13, wherein thegrooves are through holes.
 19. The method of claim 13, wherein saidquartz crystal oscillating circuit is constructed so that a ratio of anabsolute value of negative resistance, |−RL₁| of a fundamental modevibration of the amplification circuit and series resistance R₁ of thefundamental mode vibration is larger than that of an absolute value ofnegative resistance, |−RL₂| of a second overtone mode vibration of theamplification circuit and series resistance R₂ of the second overtonemode vibration.
 20. The method of claim 19, wherein comprising thefurther step of forming a plurality of individual quartz crystal tuningfork resonators in a quartz crystal wafer, each of which is capable ofvibrating in a flexural mode and said quartz crystal tuning forkresonator is one of the individual quartz crystal tuning forkresonators.
 21. The method of claim 20, wherein an output signal of saidquartz crystal oscillating circuit is outputted through a buffer circuitand has a frequency of 32.764 kHz to 32.772 kHz.
 22. The method of claim21, wherein comprising the further step of forming metal films forfrequency adjustment on a quartz crystal wafer before said tuning forktines are formed therein
 23. The method of claim 21, wherein comprisingthe further step of forming metal films for frequency adjustment on saidtuning fork tines formed in a quartz crystal wafer.
 24. The method ofclaim 21, wherein each of the individual quartz crystal tuning forkresonators comprises: tuning fork tines and a tuning fork base; groovesprovided at the tuning fork tines; and electrodes disposed inside of thegrooves and on sides of the tuning fork tines, and has resonancefrequency higher than 32.768 kHz in a fundamental mode vibration, andwherein comprising the further steps of: forming metal films on thetuning fork tines of the individual quartz crystal tuning forkresonators in the quartz crystal wafer by a spattering method or anevaporation method so as to get the individual quartz crystal tuningfork resonators each of which has resonance frequency of 29.4 kHz to32.75 kHz; after that, adjusting the resonance frequency by removing apart or all of the metal films formed on the tuning fork tines in thequartz crystal wafer by laser trimming or a plasma etching method sothat it is within a range of 32.2 kHz to 33.08 kHz; and constructingsaid quartz crystal oscillating circuit comprising the amplificationcircuit and the feedback circuit so that a ratio of an amplificationrate α₁ of a fundamental mode vibration and an amplification rate α₂ ofa second overtone mode vibration of the amplification circuit is largerthan that of a feedback rate β₂ of the second overtone mode vibrationand a feedback rate β₁ of the fundamental mode vibration of the feedbackcircuit, and a product of the amplification rate α₁ and the feedbackrate β₁ of the fundamental mode vibration is larger than
 1. 25. Themethod of claim 21, wherein each of the individual quartz crystal tuningfork resonators comprises: tuning fork tines and a tuning fork base;grooves provided at the tuning fork tines; and electrodes disposedinside of the grooves and on sides of the tuning fork tines, and hasresonance frequency higher than 32.768 kHz in a fundamental modevibration, and wherein comprising the further steps of: mounting saidquartz crystal tuning fork resonator at a mounting portion of a case ora lid by conductive adhesives or solder; adjusting the resonancefrequency by adding a metal on the tuning fork tines using anevaporation method; and forming a quartz crystal unit comprising saidquartz crystal tuning fork resonator, the case and the lid.
 26. A methodfor manufacturing a quartz crystal oscillator comprising: a quartzcrystal oscillating circuit comprising; an amplification circuitcomprising a CMOS inverter and a feedback resistor, and a feedbackcircuit comprising a quartz crystal tuning fork resonator capable ofvibrating in a flexural mode, resistors and capacitors, said quartzcrystal tuning fork resonator comprising the step of: utilizing achemical etching method to form a resonator comprising; tuning forktines each of which has a length, a width and a thickness and the lengthgreater than the width and the thickness, and a tuning fork base, andelectrodes disposed on obverse and reverse faces and sides of saidtuning fork tines so that said tuning fork tines are capable ofvibrating in inverse phase, and said quartz crystal tuning forkresonator being formed in a quartz crystal wafer and a plurality ofindividual quartz crystal tuning fork resonators capable of vibratingeach in a fundamental mode being formed therein, each of whichcomprises: tuning fork tines and a tuning fork base; and electrodesdisposed on obverse and reverse faces and sides of the tuning forktines, and has resonance frequency higher than 32.768 kHz, whereincomprising the further steps of: forming metal films on the tuning forktines of the individual quartz crystal tuning fork resonators in thequartz crystal wafer by a spattering method or an evaporation method soas to get the individual quartz crystal tuning fork resonators each ofwhich has resonance frequency of 29.4 kHz to 32.75 kHz; mounting eachresonator at a mounting portion of a case; and after that, adjusting theresonance frequency of the each resonator by laser trimming or a plasmaetching method so that it is within a range of 32.764 kHz to 32.772 kHzwhen a quartz crystal unit comprising said quartz crystal tuning forkresonator is provided, wherein said quartz crystal oscillating circuitcomprising the amplification circuit and the feedback circuit isconstructed so that a ratio of an absolute value of negative resistance,|−RL₁| of a fundamental mode vibration of the amplification circuit andseries resistance R₁ of the fundamental mode vibration is larger thanthat of an absolute value of negative resistance, |−RL₂| of a secondovertone mode vibration of the amplification circuit and seriesresistance R₂ of the second overtone mode vibration, and an outputsignal of said quartz crystal oscillating circuit is outputted through abuffer circuit and has a frequency of 32.764 kHz to 32.772 kHz, andwherein comprising the further step of inspecting the individual quartzcrystal tuning fork resonators formed in the quartz crystal wafer, andwhen there is a failure resonator therein, it is removed from the quartzcrystal wafer or something is marked on it or it is remembered by acomputer.
 27. The method of claim 26, wherein comprising the furtherstep of adjusting the resonance frequency of each resonator by removinga part or all of the metal films formed on the tuning fork tines in thequartz crystal wafer by laser trimming or a plasma etching method sothat it is within a range of 32.2 kHz to 33.08 kHz.